LMFDB - Embedded newform 2548.2.j.r.1145.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(1145,2548)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2548.1145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 10 x^{10} - 8 x^{9} + 80 x^{8} - 56 x^{7} + 220 x^{6} - 240 x^{5} + 484 x^{4} - 336 x^{3} + \cdots + 4 $ x^12 + 10x^10 - 8x^9 + 80x^8 - 56x^7 + 220x^6 - 240x^5 + 484x^4 - 336x^3 + 216x^2 - 32x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.6
Root			$-0.909151 - 1.57470i$ of defining polynomial
Character	$\chi$	$=$	2548.1145
Dual form			2548.2.j.r.1353.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61626 - 2.79944i) q^{3} +(-1.52970 - 2.64951i) q^{5} +(-3.72458 - 6.45116i) q^{9} +(2.84800 - 4.93288i) q^{11} -1.00000 q^{13} -9.88953 q^{15} +(-3.44578 + 5.96827i) q^{17} +(-1.98051 - 3.43034i) q^{19} +(0.940643 + 1.62924i) q^{23} +(-2.17993 + 3.77576i) q^{25} -14.3820 q^{27} +0.290353 q^{29} +(-0.926514 + 1.60477i) q^{31} +(-9.20620 - 15.9456i) q^{33} +(3.45419 + 5.98283i) q^{37} +(-1.61626 + 2.79944i) q^{39} +3.52487 q^{41} +9.13934 q^{43} +(-11.3949 + 19.7366i) q^{45} +(-5.03990 - 8.72936i) q^{47} +(11.1386 + 19.2925i) q^{51} +(3.90233 - 6.75903i) q^{53} -17.4263 q^{55} -12.8040 q^{57} +(5.08894 - 8.81431i) q^{59} +(3.50844 + 6.07680i) q^{61} +(1.52970 + 2.64951i) q^{65} +(1.73182 - 2.99960i) q^{67} +6.08128 q^{69} +4.29499 q^{71} +(0.108628 - 0.188149i) q^{73} +(7.04667 + 12.2052i) q^{75} +(0.0426930 + 0.0739465i) q^{79} +(-12.0713 + 20.9080i) q^{81} +6.42980 q^{83} +21.0840 q^{85} +(0.469285 - 0.812826i) q^{87} +(7.60632 + 13.1745i) q^{89} +(2.99497 + 5.18744i) q^{93} +(-6.05915 + 10.4948i) q^{95} -4.47830 q^{97} -42.4304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{5} - 6 q^{9} + 4 q^{11} - 12 q^{13} + 8 q^{15} - 16 q^{17} - 10 q^{19} + 2 q^{23} - 12 q^{25} - 24 q^{27} + 4 q^{29} - 6 q^{31} - 28 q^{33} - 16 q^{37} + 16 q^{41} + 12 q^{43} - 34 q^{45} - 30 q^{47}+ \cdots - 104 q^{99}+O(q^{100}) $ 12 * q - 10 * q^5 - 6 * q^9 + 4 * q^11 - 12 * q^13 + 8 * q^15 - 16 * q^17 - 10 * q^19 + 2 * q^23 - 12 * q^25 - 24 * q^27 + 4 * q^29 - 6 * q^31 - 28 * q^33 - 16 * q^37 + 16 * q^41 + 12 * q^43 - 34 * q^45 - 30 * q^47 + 12 * q^51 + 6 * q^53 - 32 * q^55 - 24 * q^57 - 8 * q^59 - 16 * q^61 + 10 * q^65 + 8 * q^69 - 14 * q^73 - 28 * q^75 - 14 * q^79 - 14 * q^81 - 28 * q^83 + 48 * q^85 - 24 * q^87 - 30 * q^89 + 16 * q^93 + 10 * q^95 + 44 * q^97 - 104 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.61626	−	2.79944i	0.933147	−	1.61626i	0.155242	−	0.987877i	$-0.450384\pi$
$3$	1.61626	−	2.79944i	0.933147	−	1.61626i	0.777905	−	0.628382i	$-0.216282\pi$
$4$		0			0
$5$	−1.52970	−	2.64951i	−0.684100	−	1.18490i	−0.973719	−	0.227754i	$-0.926862\pi$
$5$	−1.52970	−	2.64951i	−0.684100	−	1.18490i	0.289618	−	0.957142i	$-0.406472\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.72458	−	6.45116i	−1.24153	−	2.15039i
$10$		0			0
$11$	2.84800	−	4.93288i	0.858704	−	1.48732i	−0.0144624	−	0.999895i	$-0.504604\pi$
$11$	2.84800	−	4.93288i	0.858704	−	1.48732i	0.873166	−	0.487423i	$-0.162063\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−9.88953			−2.55347
$16$		0			0
$17$	−3.44578	+	5.96827i	−0.835725	+	1.44752i	0.0577133	+	0.998333i	$0.481619\pi$
$17$	−3.44578	+	5.96827i	−0.835725	+	1.44752i	−0.893439	+	0.449185i	$0.851714\pi$
$18$		0			0
$19$	−1.98051	−	3.43034i	−0.454360	−	0.786974i	0.544291	−	0.838896i	$-0.316799\pi$
$19$	−1.98051	−	3.43034i	−0.454360	−	0.786974i	−0.998651	+	0.0519221i	$0.983465\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.940643	+	1.62924i	0.196138	+	0.339720i	0.947273	−	0.320428i	$-0.103827\pi$
$23$	0.940643	+	1.62924i	0.196138	+	0.339720i	−0.751135	+	0.660148i	$0.770493\pi$
$24$		0			0
$25$	−2.17993	+	3.77576i	−0.435987	+	0.755151i
$26$		0			0
$27$	−14.3820			−2.76781
$28$		0			0
$29$	0.290353			0.0539172			0.0269586	−	0.999637i	$-0.491418\pi$
$29$	0.290353			0.0539172			0.0269586	+	0.999637i	$0.491418\pi$
$30$		0			0
$31$	−0.926514	+	1.60477i	−0.166407	+	0.288225i	−0.937154	−	0.348916i	$-0.886550\pi$
$31$	−0.926514	+	1.60477i	−0.166407	+	0.288225i	0.770747	+	0.637141i	$0.219883\pi$
$32$		0			0
$33$	−9.20620	−	15.9456i	−1.60259	−	2.77577i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.45419	+	5.98283i	0.567865	+	0.983572i	0.996777	+	0.0802252i	$0.0255639\pi$
$37$	3.45419	+	5.98283i	0.567865	+	0.983572i	−0.428911	+	0.903347i	$0.641103\pi$
$38$		0			0
$39$	−1.61626	+	2.79944i	−0.258808	+	0.448269i
$40$		0			0
$41$	3.52487			0.550492			0.275246	−	0.961374i	$-0.411241\pi$
$41$	3.52487			0.550492			0.275246	+	0.961374i	$0.411241\pi$
$42$		0			0
$43$	9.13934			1.39374			0.696868	−	0.717199i	$-0.254576\pi$
$43$	9.13934			1.39374			0.696868	+	0.717199i	$0.254576\pi$
$44$		0			0
$45$	−11.3949	+	19.7366i	−1.69866	+	2.94216i
$46$		0			0
$47$	−5.03990	−	8.72936i	−0.735145	−	1.27331i	−0.954660	−	0.297699i	$-0.903781\pi$
$47$	−5.03990	−	8.72936i	−0.735145	−	1.27331i	0.219515	−	0.975609i	$-0.429552\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	11.1386	+	19.2925i	1.55971	+	2.70150i
$52$		0			0
$53$	3.90233	−	6.75903i	0.536026	−	0.928424i	−0.463087	−	0.886313i	$-0.653258\pi$
$53$	3.90233	−	6.75903i	0.536026	−	0.928424i	0.999113	−	0.0421110i	$-0.0134083\pi$
$54$		0			0
$55$	−17.4263			−2.34976
$56$		0			0
$57$	−12.8040			−1.69594
$58$		0			0
$59$	5.08894	−	8.81431i	0.662524	−	1.14752i	−0.317427	−	0.948283i	$-0.602819\pi$
$59$	5.08894	−	8.81431i	0.662524	−	1.14752i	0.979950	−	0.199242i	$-0.0638480\pi$
$60$		0			0
$61$	3.50844	+	6.07680i	0.449210	+	0.778054i	0.998335	−	0.0576862i	$-0.0183723\pi$
$61$	3.50844	+	6.07680i	0.449210	+	0.778054i	−0.549125	+	0.835740i	$0.685039\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.52970	+	2.64951i	0.189735	+	0.328631i
$66$		0			0
$67$	1.73182	−	2.99960i	0.211575	−	0.366459i	−0.740632	−	0.671910i	$-0.765474\pi$
$67$	1.73182	−	2.99960i	0.211575	−	0.366459i	0.952208	+	0.305451i	$0.0988073\pi$
$68$		0			0
$69$	6.08128			0.732101
$70$		0			0
$71$	4.29499			0.509721			0.254861	−	0.966978i	$-0.417970\pi$
$71$	4.29499			0.509721			0.254861	+	0.966978i	$0.417970\pi$
$72$		0			0
$73$	0.108628	−	0.188149i	0.0127139	−	0.0220211i	−0.859598	−	0.510970i	$-0.829286\pi$
$73$	0.108628	−	0.188149i	0.0127139	−	0.0220211i	0.872312	+	0.488949i	$0.162620\pi$
$74$		0			0
$75$	7.04667	+	12.2052i	0.813680	+	1.40933i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.0426930	+	0.0739465i	0.00480334	+	0.00831963i	0.868417	−	0.495834i	$-0.165138\pi$
$79$	0.0426930	+	0.0739465i	0.00480334	+	0.00831963i	−0.863614	+	0.504154i	$0.831804\pi$
$80$		0			0
$81$	−12.0713	+	20.9080i	−1.34125	+	2.32311i
$82$		0			0
$83$	6.42980			0.705762			0.352881	−	0.935668i	$-0.385202\pi$
$83$	6.42980			0.705762			0.352881	+	0.935668i	$0.385202\pi$
$84$		0			0
$85$	21.0840			2.28688
$86$		0			0
$87$	0.469285	−	0.812826i	0.0503127	−	0.0871441i
$88$		0			0
$89$	7.60632	+	13.1745i	0.806268	+	1.39650i	0.915432	+	0.402473i	$0.131849\pi$
$89$	7.60632	+	13.1745i	0.806268	+	1.39650i	−0.109164	+	0.994024i	$0.534817\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.99497	+	5.18744i	0.310564	+	0.537913i
$94$		0			0
$95$	−6.05915	+	10.4948i	−0.621655	+	1.07674i
$96$		0			0
$97$	−4.47830			−0.454702			−0.227351	−	0.973813i	$-0.573006\pi$
$97$	−4.47830			−0.454702			−0.227351	+	0.973813i	$0.573006\pi$
$98$		0			0
$99$	−42.4304			−4.26441
$100$		0			0
$101$	−9.67830	+	16.7633i	−0.963027	+	1.66801i	−0.248201	+	0.968708i	$0.579839\pi$
$101$	−9.67830	+	16.7633i	−0.963027	+	1.66801i	−0.714825	+	0.699303i	$0.753494\pi$
$102$		0			0
$103$	−9.63351	−	16.6857i	−0.949218	−	1.64409i	−0.747077	−	0.664737i	$-0.768544\pi$
$103$	−9.63351	−	16.6857i	−0.949218	−	1.64409i	−0.202141	−	0.979357i	$-0.564790\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.33890	−	16.1754i	−0.902825	−	1.56374i	−0.823810	−	0.566866i	$-0.808156\pi$
$107$	−9.33890	−	16.1754i	−0.902825	−	1.56374i	−0.0790156	−	0.996873i	$-0.525178\pi$
$108$		0			0
$109$	−0.969207	+	1.67872i	−0.0928332	+	0.160792i	−0.908702	−	0.417445i	$-0.862926\pi$
$109$	−0.969207	+	1.67872i	−0.0928332	+	0.160792i	0.815869	+	0.578237i	$0.196259\pi$
$110$		0			0
$111$	22.3315			2.11961
$112$		0			0
$113$	1.26493			0.118994			0.0594971	−	0.998228i	$-0.481050\pi$
$113$	1.26493			0.118994			0.0594971	+	0.998228i	$0.481050\pi$
$114$		0			0
$115$	2.87779	−	4.98448i	0.268356	−	0.464805i
$116$		0			0
$117$	3.72458	+	6.45116i	0.344338	+	0.596410i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.7222	−	18.5714i	−0.974744	−	1.68831i
$122$		0			0
$123$	5.69709	−	9.86766i	0.513690	−	0.889737i
$124$		0			0
$125$	−1.95841			−0.175166
$126$		0			0
$127$	−8.86261			−0.786429			−0.393215	−	0.919447i	$-0.628637\pi$
$127$	−8.86261			−0.786429			−0.393215	+	0.919447i	$0.628637\pi$
$128$		0			0
$129$	14.7715	−	25.5851i	1.30056	−	2.25264i
$130$		0			0
$131$	−7.70628	−	13.3477i	−0.673301	−	1.16619i	−0.976963	−	0.213411i	$-0.931543\pi$
$131$	−7.70628	−	13.3477i	−0.673301	−	1.16619i	0.303662	−	0.952780i	$-0.401791\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	22.0001	+	38.1052i	1.89346	+	3.27957i
$136$		0			0
$137$	2.08592	−	3.61293i	0.178213	−	0.308673i	−0.763056	−	0.646333i	$-0.776302\pi$
$137$	2.08592	−	3.61293i	0.178213	−	0.308673i	0.941268	+	0.337659i	$0.109635\pi$
$138$		0			0
$139$	−2.53405			−0.214935			−0.107468	−	0.994209i	$-0.534274\pi$
$139$	−2.53405			−0.214935			−0.107468	+	0.994209i	$0.534274\pi$
$140$		0			0
$141$	−32.5831			−2.74399
$142$		0			0
$143$	−2.84800	+	4.93288i	−0.238162	+	0.412508i
$144$		0			0
$145$	−0.444152	−	0.769293i	−0.0368848	−	0.0638863i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.79002	+	6.56451i	0.310491	+	0.537785i	0.978469	−	0.206396i	$-0.0661734\pi$
$149$	3.79002	+	6.56451i	0.310491	+	0.537785i	−0.667978	+	0.744181i	$0.732840\pi$
$150$		0			0
$151$	−8.12602	+	14.0747i	−0.661286	+	1.14538i	0.318992	+	0.947757i	$0.396656\pi$
$151$	−8.12602	+	14.0747i	−0.661286	+	1.14538i	−0.980278	+	0.197623i	$0.936678\pi$
$152$		0			0
$153$	51.3364			4.15030
$154$		0			0
$155$	5.66913			0.455356
$156$		0			0
$157$	−8.90496	+	15.4238i	−0.710693	+	1.23096i	0.253904	+	0.967229i	$0.418285\pi$
$157$	−8.90496	+	15.4238i	−0.710693	+	1.23096i	−0.964597	+	0.263727i	$0.915048\pi$
$158$		0			0
$159$	−12.6143	−	21.8487i	−1.00038	−	1.73271i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.52022	−	4.36514i	−0.197399	−	0.341905i	0.750286	−	0.661114i	$-0.229916\pi$
$163$	−2.52022	−	4.36514i	−0.197399	−	0.341905i	−0.947684	+	0.319209i	$0.896583\pi$
$164$		0			0
$165$	−28.1654	+	48.7838i	−2.19267	+	3.79782i
$166$		0			0
$167$	19.3736			1.49917			0.749586	−	0.661907i	$-0.230253\pi$
$167$	19.3736			1.49917			0.749586	+	0.661907i	$0.230253\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−14.7531	+	25.5532i	−1.12820	+	1.95410i
$172$		0			0
$173$	−3.31203	−	5.73661i	−0.251809	−	0.436146i	0.712215	−	0.701961i	$-0.247692\pi$
$173$	−3.31203	−	5.73661i	−0.251809	−	0.436146i	−0.964024	+	0.265815i	$0.914359\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−16.4501	−	28.4924i	−1.23646	−	2.14162i
$178$		0			0
$179$	−1.27330	+	2.20541i	−0.0951706	+	0.164840i	−0.909680	−	0.415310i	$-0.863673\pi$
$179$	−1.27330	+	2.20541i	−0.0951706	+	0.164840i	0.814509	+	0.580151i	$0.197006\pi$
$180$		0			0
$181$	5.21116			0.387342			0.193671	−	0.981067i	$-0.437961\pi$
$181$	5.21116			0.387342			0.193671	+	0.981067i	$0.437961\pi$
$182$		0			0
$183$	22.6822			1.67671
$184$		0			0
$185$	10.5677	−	18.3038i	0.776954	−	1.34572i
$186$		0			0
$187$	19.6272	+	33.9953i	1.43528	+	2.48598i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.24741	+	10.8208i	0.452047	+	0.782968i	0.998513	−	0.0545133i	$-0.0173607\pi$
$191$	6.24741	+	10.8208i	0.452047	+	0.782968i	−0.546466	+	0.837481i	$0.684027\pi$
$192$		0			0
$193$	−8.30778	+	14.3895i	−0.598007	+	1.03578i	0.395108	+	0.918635i	$0.370707\pi$
$193$	−8.30778	+	14.3895i	−0.598007	+	1.03578i	−0.993115	+	0.117144i	$0.962626\pi$
$194$		0			0
$195$	9.88953			0.708204
$196$		0			0
$197$	17.8588			1.27239			0.636194	−	0.771529i	$-0.280508\pi$
$197$	17.8588			1.27239			0.636194	+	0.771529i	$0.280508\pi$
$198$		0			0
$199$	−6.52315	+	11.2984i	−0.462414	+	0.800925i	−0.999081	−	0.0428697i	$-0.986350\pi$
$199$	−6.52315	+	11.2984i	−0.462414	+	0.800925i	0.536667	+	0.843794i	$0.319683\pi$
$200$		0			0
$201$	−5.59813	−	9.69625i	−0.394862	−	0.683921i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.39197	−	9.33917i	−0.376592	−	0.652276i
$206$		0			0
$207$	7.00700	−	12.1365i	0.487020	−	0.843543i
$208$		0			0
$209$	−22.5619			−1.56064
$210$		0			0
$211$	7.02031			0.483298			0.241649	−	0.970364i	$-0.422312\pi$
$211$	7.02031			0.483298			0.241649	+	0.970364i	$0.422312\pi$
$212$		0			0
$213$	6.94181	−	12.0236i	0.475645	−	0.823841i
$214$		0			0
$215$	−13.9804	−	24.2148i	−0.953456	−	1.65143i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.351141	−	0.608194i	−0.0237279	−	0.0410979i
$220$		0			0
$221$	3.44578	−	5.96827i	0.231788	−	0.401469i
$222$		0			0
$223$	−5.96462			−0.399421			−0.199710	−	0.979855i	$-0.564000\pi$
$223$	−5.96462			−0.399421			−0.199710	+	0.979855i	$0.564000\pi$
$224$		0			0
$225$	32.4774			2.16516
$226$		0			0
$227$	0.802274	−	1.38958i	0.0532488	−	0.0922296i	−0.838172	−	0.545405i	$-0.816376\pi$
$227$	0.802274	−	1.38958i	0.0532488	−	0.0922296i	0.891421	+	0.453176i	$0.149709\pi$
$228$		0			0
$229$	5.05571	+	8.75674i	0.334090	+	0.578662i	0.983310	−	0.181940i	$-0.0582376\pi$
$229$	5.05571	+	8.75674i	0.334090	+	0.578662i	−0.649219	+	0.760601i	$0.724904\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.87567	+	3.24876i	0.122879	+	0.212833i	0.920902	−	0.389794i	$-0.127454\pi$
$233$	1.87567	+	3.24876i	0.122879	+	0.212833i	−0.798023	+	0.602628i	$0.794120\pi$
$234$		0			0
$235$	−15.4190	+	26.7065i	−1.00583	+	1.74214i
$236$		0			0
$237$	0.276012			0.0179289
$238$		0			0
$239$	24.4433			1.58111			0.790554	−	0.612392i	$-0.209793\pi$
$239$	24.4433			1.58111			0.790554	+	0.612392i	$0.209793\pi$
$240$		0			0
$241$	−0.872936	+	1.51197i	−0.0562307	+	0.0973945i	−0.892771	−	0.450512i	$-0.851242\pi$
$241$	−0.872936	+	1.51197i	−0.0562307	+	0.0973945i	0.836540	+	0.547906i	$0.184575\pi$
$242$		0			0
$243$	17.4476	+	30.2201i	1.11926	+	1.93862i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.98051	+	3.43034i	0.126017	+	0.218267i
$248$		0			0
$249$	10.3922	−	17.9998i	0.658580	−	1.14069i
$250$		0			0
$251$	−0.612437			−0.0386567			−0.0193283	−	0.999813i	$-0.506153\pi$
$251$	−0.612437			−0.0386567			−0.0193283	+	0.999813i	$0.506153\pi$
$252$		0			0
$253$	10.7158			0.673696
$254$		0			0
$255$	34.0772	−	59.0234i	2.13400	−	3.69619i
$256$		0			0
$257$	−8.28173	−	14.3444i	−0.516600	−	0.894778i	−0.999814	−	0.0192754i	$-0.993864\pi$
$257$	−8.28173	−	14.3444i	−0.516600	−	0.894778i	0.483214	−	0.875502i	$-0.339469\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.08144	−	1.87311i	−0.0669396	−	0.115943i
$262$		0			0
$263$	−0.504110	+	0.873144i	−0.0310847	+	0.0538404i	−0.881149	−	0.472838i	$-0.843230\pi$
$263$	−0.504110	+	0.873144i	−0.0310847	+	0.0538404i	0.850065	+	0.526679i	$0.176563\pi$
$264$		0			0
$265$	−23.8775			−1.46678
$266$		0			0
$267$	49.1751			3.00947
$268$		0			0
$269$	13.2216	−	22.9005i	0.806137	−	1.39627i	−0.109384	−	0.994000i	$-0.534888\pi$
$269$	13.2216	−	22.9005i	0.806137	−	1.39627i	0.915521	−	0.402270i	$-0.131779\pi$
$270$		0			0
$271$	−4.41942	−	7.65465i	−0.268460	−	0.464987i	0.700004	−	0.714139i	$-0.253181\pi$
$271$	−4.41942	−	7.65465i	−0.268460	−	0.464987i	−0.968464	+	0.249152i	$0.919848\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.4169	+	21.5067i	0.748767	+	1.29690i
$276$		0			0
$277$	0.755322	−	1.30826i	0.0453829	−	0.0786055i	−0.842442	−	0.538788i	$-0.818883\pi$
$277$	0.755322	−	1.30826i	0.0453829	−	0.0786055i	0.887825	+	0.460182i	$0.152216\pi$
$278$		0			0
$279$	13.8035			0.826394
$280$		0			0
$281$	−12.9564			−0.772915			−0.386457	−	0.922307i	$-0.626301\pi$
$281$	−12.9564			−0.772915			−0.386457	+	0.922307i	$0.626301\pi$
$282$		0			0
$283$	3.28796	−	5.69491i	0.195449	−	0.338528i	−0.751599	−	0.659621i	$-0.770717\pi$
$283$	3.28796	−	5.69491i	0.195449	−	0.338528i	0.947048	+	0.321093i	$0.104050\pi$
$284$		0			0
$285$	19.5863	+	33.9245i	1.16019	+	2.00951i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−15.2468	−	26.4083i	−0.896873	−	1.55343i
$290$		0			0
$291$	−7.23808	+	12.5367i	−0.424304	+	0.734916i
$292$		0			0
$293$	8.96860			0.523951			0.261976	−	0.965074i	$-0.415626\pi$
$293$	8.96860			0.523951			0.261976	+	0.965074i	$0.415626\pi$
$294$		0			0
$295$	−31.1381			−1.81293
$296$		0			0
$297$	−40.9599	+	70.9446i	−2.37673	+	4.11662i
$298$		0			0
$299$	−0.940643	−	1.62924i	−0.0543988	−	0.0942214i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	31.2853	+	54.1877i	1.79729	+	3.11300i
$304$		0			0
$305$	10.7337	−	18.5913i	0.614609	−	1.06453i
$306$		0			0
$307$	7.15347			0.408270			0.204135	−	0.978943i	$-0.434562\pi$
$307$	7.15347			0.408270			0.204135	+	0.978943i	$0.434562\pi$
$308$		0			0
$309$	−62.2810			−3.54304
$310$		0			0
$311$	4.18901	−	7.25558i	0.237537	−	0.411426i	−0.722470	−	0.691402i	$-0.756993\pi$
$311$	4.18901	−	7.25558i	0.237537	−	0.411426i	0.960007	+	0.279976i	$0.0903266\pi$
$312$		0			0
$313$	−15.9774	−	27.6737i	−0.903098	−	1.56421i	−0.823450	−	0.567389i	$-0.807954\pi$
$313$	−15.9774	−	27.6737i	−0.903098	−	1.56421i	−0.0796483	−	0.996823i	$-0.525380\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.47491	−	16.4110i	−0.532164	−	0.921735i	−0.999295	−	0.0375467i	$-0.988046\pi$
$317$	−9.47491	−	16.4110i	−0.532164	−	0.921735i	0.467131	−	0.884188i	$-0.345288\pi$
$318$		0			0
$319$	0.826925	−	1.43228i	0.0462989	−	0.0801920i
$320$		0			0
$321$	−60.3763			−3.36988
$322$		0			0
$323$	27.2976			1.51888
$324$		0			0
$325$	2.17993	−	3.77576i	0.120921	−	0.209441i
$326$		0			0
$327$	3.13298	+	5.42647i	0.173254	+	0.300085i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.83171	+	3.17261i	0.100680	+	0.174382i	0.911965	−	0.410268i	$-0.134565\pi$
$331$	1.83171	+	3.17261i	0.100680	+	0.174382i	−0.811285	+	0.584651i	$0.801232\pi$
$332$		0			0
$333$	25.7308	−	44.5671i	1.41004	−	2.44226i
$334$		0			0
$335$	−10.5966			−0.578955
$336$		0			0
$337$	−20.2274			−1.10186			−0.550928	−	0.834553i	$-0.685726\pi$
$337$	−20.2274			−1.10186			−0.550928	+	0.834553i	$0.685726\pi$
$338$		0			0
$339$	2.04445	−	3.54108i	0.111039	−	0.192325i
$340$		0			0
$341$	5.27742	+	9.14076i	0.285788	+	0.495000i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.30251	−	16.1124i	−0.500830	−	0.867464i
$346$		0			0
$347$	1.65290	−	2.86291i	0.0887324	−	0.153689i	−0.818243	−	0.574872i	$-0.805052\pi$
$347$	1.65290	−	2.86291i	0.0887324	−	0.153689i	0.906976	+	0.421183i	$0.138385\pi$
$348$		0			0
$349$	−6.89971			−0.369333			−0.184666	−	0.982801i	$-0.559120\pi$
$349$	−6.89971			−0.369333			−0.184666	+	0.982801i	$0.559120\pi$
$350$		0			0
$351$	14.3820			0.767654
$352$		0			0
$353$	−1.64537	+	2.84987i	−0.0875742	+	0.151683i	−0.906485	−	0.422237i	$-0.861245\pi$
$353$	−1.64537	+	2.84987i	−0.0875742	+	0.151683i	0.818911	+	0.573921i	$0.194578\pi$
$354$		0			0
$355$	−6.57002	−	11.3796i	−0.348701	−	0.603967i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.48507	+	7.76837i	0.236713	+	0.409999i	0.959769	−	0.280790i	$-0.0905965\pi$
$359$	4.48507	+	7.76837i	0.236713	+	0.409999i	−0.723056	+	0.690789i	$0.757263\pi$
$360$		0			0
$361$	1.65517	−	2.86685i	0.0871144	−	0.150887i
$362$		0			0
$363$	−69.3192			−3.63832
$364$		0			0
$365$	−0.664669			−0.0347904
$366$		0			0
$367$	10.8730	−	18.8326i	0.567566	−	0.983054i	−0.429239	−	0.903191i	$-0.641218\pi$
$367$	10.8730	−	18.8326i	0.567566	−	0.983054i	0.996806	−	0.0798631i	$-0.0254483\pi$
$368$		0			0
$369$	−13.1286	−	22.7395i	−0.683450	−	1.18377i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.01642	−	10.4208i	−0.311519	−	0.539566i	0.667173	−	0.744903i	$-0.267504\pi$
$373$	−6.01642	−	10.4208i	−0.311519	−	0.539566i	−0.978691	+	0.205337i	$0.934171\pi$
$374$		0			0
$375$	−3.16530	+	5.48247i	−0.163456	+	0.283113i
$376$		0			0
$377$	−0.290353			−0.0149539
$378$		0			0
$379$	−36.8399			−1.89234			−0.946170	−	0.323671i	$-0.895083\pi$
$379$	−36.8399			−1.89234			−0.946170	+	0.323671i	$0.895083\pi$
$380$		0			0
$381$	−14.3243	+	24.8103i	−0.733854	+	1.27107i
$382$		0			0
$383$	3.85518	+	6.67737i	0.196991	+	0.341198i	0.947551	−	0.319604i	$-0.103550\pi$
$383$	3.85518	+	6.67737i	0.196991	+	0.341198i	−0.750561	+	0.660802i	$0.770216\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−34.0402	−	58.9594i	−1.73036	−	2.99707i
$388$		0			0
$389$	−15.0435	+	26.0562i	−0.762738	+	1.32110i	0.178697	+	0.983904i	$0.442812\pi$
$389$	−15.0435	+	26.0562i	−0.762738	+	1.32110i	−0.941434	+	0.337196i	$0.890521\pi$
$390$		0			0
$391$	−12.9650			−0.655668
$392$		0			0
$393$	−49.8213			−2.51315
$394$		0			0
$395$	0.130615	−	0.226231i	0.00657193	−	0.0113829i
$396$		0			0
$397$	−2.90071	−	5.02417i	−0.145582	−	0.252156i	0.784008	−	0.620751i	$-0.213172\pi$
$397$	−2.90071	−	5.02417i	−0.145582	−	0.252156i	−0.929590	+	0.368595i	$0.879839\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.480697	−	0.832592i	−0.0240049	−	0.0415777i	0.853773	−	0.520645i	$-0.174308\pi$
$401$	−0.480697	−	0.832592i	−0.0240049	−	0.0415777i	−0.877778	+	0.479067i	$0.840975\pi$
$402$		0			0
$403$	0.926514	−	1.60477i	0.0461529	−	0.0799392i
$404$		0			0
$405$	73.8614			3.67020
$406$		0			0
$407$	39.3501			1.95051
$408$		0			0
$409$	13.5007	−	23.3839i	0.667567	−	1.15626i	−0.311015	−	0.950405i	$-0.600669\pi$
$409$	13.5007	−	23.3839i	0.667567	−	1.15626i	0.978582	−	0.205856i	$-0.0659977\pi$
$410$		0			0
$411$	−6.74278	−	11.6788i	−0.332597	−	0.576075i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.83563	−	17.0358i	−0.482812	−	0.836255i
$416$		0			0
$417$	−4.09568	+	7.09392i	−0.200566	+	0.347391i
$418$		0			0
$419$	−19.5024			−0.952752			−0.476376	−	0.879242i	$-0.658050\pi$
$419$	−19.5024			−0.952752			−0.476376	+	0.879242i	$0.658050\pi$
$420$		0			0
$421$	7.57400			0.369134			0.184567	−	0.982820i	$-0.440912\pi$
$421$	7.57400			0.369134			0.184567	+	0.982820i	$0.440912\pi$
$422$		0			0
$423$	−37.5430	+	65.0264i	−1.82540	+	3.16169i
$424$		0			0
$425$	−15.0232	−	26.0209i	−0.728730	−	1.26220i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	9.20620	+	15.9456i	0.444479	+	0.769861i
$430$		0			0
$431$	14.3179	−	24.7994i	0.689670	−	1.19454i	−0.282274	−	0.959334i	$-0.591089\pi$
$431$	14.3179	−	24.7994i	0.689670	−	1.19454i	0.971944	−	0.235210i	$-0.0755779\pi$
$432$		0			0
$433$	31.4561			1.51169			0.755843	−	0.654753i	$-0.227227\pi$
$433$	31.4561			1.51169			0.755843	+	0.654753i	$0.227227\pi$
$434$		0			0
$435$	−2.87145			−0.137676
$436$		0			0
$437$	3.72590	−	6.45345i	0.178234	−	0.308710i
$438$		0			0
$439$	4.39415	+	7.61089i	0.209721	+	0.363248i	0.951627	−	0.307257i	$-0.0994110\pi$
$439$	4.39415	+	7.61089i	0.209721	+	0.363248i	−0.741905	+	0.670505i	$0.766078\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.7401	−	23.7985i	−0.652811	−	1.13070i	−0.982438	−	0.186591i	$-0.940256\pi$
$443$	−13.7401	−	23.7985i	−0.652811	−	1.13070i	0.329626	−	0.944112i	$-0.393077\pi$
$444$		0			0
$445$	23.2707	−	40.3060i	1.10314	−	1.91069i
$446$		0			0
$447$	24.5026			1.15893
$448$		0			0
$449$	−13.0938			−0.617933			−0.308966	−	0.951073i	$-0.599983\pi$
$449$	−13.0938			−0.617933			−0.308966	+	0.951073i	$0.599983\pi$
$450$		0			0
$451$	10.0388	−	17.3877i	0.472709	−	0.818756i
$452$		0			0
$453$	26.2675	+	45.4966i	1.23415	+	2.13762i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.6590	−	30.5863i	−0.826053	−	1.43077i	−0.901112	−	0.433587i	$-0.857248\pi$
$457$	−17.6590	−	30.5863i	−0.826053	−	1.43077i	0.0750590	−	0.997179i	$-0.476085\pi$
$458$		0			0
$459$	49.5572	−	85.8356i	2.31313	−	4.00646i
$460$		0			0
$461$	29.4052			1.36954			0.684768	−	0.728761i	$-0.259904\pi$
$461$	29.4052			1.36954			0.684768	+	0.728761i	$0.259904\pi$
$462$		0			0
$463$	−26.9196			−1.25106			−0.625531	−	0.780199i	$-0.715118\pi$
$463$	−26.9196			−1.25106			−0.625531	+	0.780199i	$0.715118\pi$
$464$		0			0
$465$	9.16278	−	15.8704i	0.424914	−	0.735972i
$466$		0			0
$467$	12.2370	+	21.1951i	0.566260	+	0.980792i	0.996931	+	0.0782828i	$0.0249437\pi$
$467$	12.2370	+	21.1951i	0.566260	+	0.980792i	−0.430671	+	0.902509i	$0.641723\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	28.7854	+	49.8578i	1.32636	+	2.29733i
$472$		0			0
$473$	26.0288	−	45.0833i	1.19681	−	2.07293i
$474$		0			0
$475$	17.2695			0.792379
$476$		0			0
$477$	−58.1381			−2.66196
$478$		0			0
$479$	−3.84091	+	6.65265i	−0.175496	+	0.303967i	−0.940333	−	0.340257i	$-0.889486\pi$
$479$	−3.84091	+	6.65265i	−0.175496	+	0.303967i	0.764837	+	0.644224i	$0.222819\pi$
$480$		0			0
$481$	−3.45419	−	5.98283i	−0.157498	−	0.272794i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.85043	+	11.8653i	0.311062	+	0.538775i
$486$		0			0
$487$	10.6737	−	18.4874i	0.483672	−	0.837744i	−0.516152	−	0.856497i	$-0.672636\pi$
$487$	10.6737	−	18.4874i	0.483672	−	0.837744i	0.999824	+	0.0187524i	$0.00596944\pi$
$488$		0			0
$489$	−16.2933			−0.736808
$490$		0			0
$491$	24.8348			1.12078			0.560390	−	0.828229i	$-0.310651\pi$
$491$	24.8348			1.12078			0.560390	+	0.828229i	$0.310651\pi$
$492$		0			0
$493$	−1.00049	+	1.73291i	−0.0450600	+	0.0780461i
$494$		0			0
$495$	64.9056	+	112.420i	2.91729	+	5.05289i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	13.3446	+	23.1136i	0.597388	+	1.03471i	0.993205	+	0.116377i	$0.0371280\pi$
$499$	13.3446	+	23.1136i	0.597388	+	1.03471i	−0.395817	+	0.918329i	$0.629539\pi$
$500$		0			0
$501$	31.3127	−	54.2352i	1.39895	−	2.42305i
$502$		0			0
$503$	−6.99840			−0.312043			−0.156022	−	0.987754i	$-0.549867\pi$
$503$	−6.99840			−0.312043			−0.156022	+	0.987754i	$0.549867\pi$
$504$		0			0
$505$	59.2194			2.63523
$506$		0			0
$507$	1.61626	−	2.79944i	0.0717805	−	0.124328i
$508$		0			0
$509$	−14.3401	−	24.8378i	−0.635613	−	1.10091i	−0.986385	−	0.164453i	$-0.947414\pi$
$509$	−14.3401	−	24.8378i	−0.635613	−	1.10091i	0.350772	−	0.936461i	$-0.385919\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	28.4836	+	49.3351i	1.25758	+	2.17820i
$514$		0			0
$515$	−29.4727	+	51.0482i	−1.29872	+	2.24945i
$516$		0			0
$517$	−57.4145			−2.52509
$518$		0			0
$519$	−21.4124			−0.939899
$520$		0			0
$521$	−15.2965	+	26.4943i	−0.670150	+	1.16073i	0.307711	+	0.951480i	$0.400437\pi$
$521$	−15.2965	+	26.4943i	−0.670150	+	1.16073i	−0.977861	+	0.209254i	$0.932896\pi$
$522$		0			0
$523$	−4.97617	−	8.61897i	−0.217593	−	0.376881i	0.736479	−	0.676461i	$-0.236487\pi$
$523$	−4.97617	−	8.61897i	−0.217593	−	0.376881i	−0.954071	+	0.299579i	$0.903154\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.38513	−	11.0594i	−0.278141	−	0.481754i
$528$		0			0
$529$	9.73038	−	16.8535i	0.423060	−	0.732762i
$530$		0			0
$531$	−75.8167			−3.29016
$532$		0			0
$533$	−3.52487			−0.152679
$534$		0			0
$535$	−28.5713	+	49.4870i	−1.23525	+	2.13951i
$536$		0			0
$537$	4.11595	+	7.12903i	0.177616	+	0.307641i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−4.95652	−	8.58495i	−0.213098	−	0.369096i	0.739585	−	0.673063i	$-0.235022\pi$
$541$	−4.95652	−	8.58495i	−0.213098	−	0.369096i	−0.952682	+	0.303968i	$0.901689\pi$
$542$		0			0
$543$	8.42257	−	14.5883i	0.361447	−	0.626045i
$544$		0			0
$545$	5.93036			0.254029
$546$		0			0
$547$	−6.50321			−0.278057			−0.139029	−	0.990288i	$-0.544398\pi$
$547$	−6.50321			−0.278057			−0.139029	+	0.990288i	$0.544398\pi$
$548$		0			0
$549$	26.1349	−	45.2670i	1.11541	−	1.93195i
$550$		0			0
$551$	−0.575047	−	0.996010i	−0.0244978	−	0.0424314i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−34.1603	−	59.1674i	−1.45002	−	2.51152i
$556$		0			0
$557$	0.958273	−	1.65978i	0.0406033	−	0.0703270i	−0.845010	−	0.534751i	$-0.820405\pi$
$557$	0.958273	−	1.65978i	0.0406033	−	0.0703270i	0.885613	+	0.464424i	$0.153739\pi$
$558$		0			0
$559$	−9.13934			−0.386553
$560$		0			0
$561$	126.890			5.35731
$562$		0			0
$563$	5.59916	−	9.69803i	0.235977	−	0.408723i	−0.723580	−	0.690241i	$-0.757504\pi$
$563$	5.59916	−	9.69803i	0.235977	−	0.408723i	0.959556	+	0.281518i	$0.0908378\pi$
$564$		0			0
$565$	−1.93495	−	3.35143i	−0.0814040	−	0.140996i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.30378	+	9.18642i	0.222346	+	0.385115i	0.955520	−	0.294927i	$-0.0952952\pi$
$569$	5.30378	+	9.18642i	0.222346	+	0.385115i	−0.733174	+	0.680041i	$0.761962\pi$
$570$		0			0
$571$	−13.5187	+	23.4150i	−0.565739	+	0.979888i	0.431242	+	0.902236i	$0.358076\pi$
$571$	−13.5187	+	23.4150i	−0.565739	+	0.979888i	−0.996981	+	0.0776516i	$0.975258\pi$
$572$		0			0
$573$	40.3897			1.68730
$574$		0			0
$575$	−8.20215			−0.342053
$576$		0			0
$577$	−3.81639	+	6.61018i	−0.158878	+	0.275186i	−0.934465	−	0.356056i	$-0.884121\pi$
$577$	−3.81639	+	6.61018i	−0.158878	+	0.275186i	0.775586	+	0.631242i	$0.217454\pi$
$578$		0			0
$579$	26.8550	+	46.5143i	1.11606	+	1.93307i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−22.2276	−	38.4994i	−0.920574	−	1.59448i
$584$		0			0
$585$	11.3949	−	19.7366i	0.471123	−	0.816009i
$586$		0			0
$587$	−15.3524			−0.633663			−0.316832	−	0.948482i	$-0.602619\pi$
$587$	−15.3524			−0.633663			−0.316832	+	0.948482i	$0.602619\pi$
$588$		0			0
$589$	7.33987			0.302434
$590$		0			0
$591$	28.8645	−	49.9947i	1.18733	−	2.05651i
$592$		0			0
$593$	−10.5632	−	18.2961i	−0.433780	−	0.751329i	0.563415	−	0.826174i	$-0.309487\pi$
$593$	−10.5632	−	18.2961i	−0.433780	−	0.751329i	−0.997195	+	0.0748447i	$0.976154\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	21.0862	+	36.5224i	0.863001	+	1.49476i
$598$		0			0
$599$	3.77676	−	6.54155i	0.154314	−	0.267280i	−0.778495	−	0.627651i	$-0.784016\pi$
$599$	3.77676	−	6.54155i	0.154314	−	0.267280i	0.932809	+	0.360371i	$0.117350\pi$
$600$		0			0
$601$	7.92867			0.323417			0.161709	−	0.986839i	$-0.448300\pi$
$601$	7.92867			0.323417			0.161709	+	0.986839i	$0.448300\pi$
$602$		0			0
$603$	−25.8012			−1.05071
$604$		0			0
$605$	−32.8033	+	56.8170i	−1.33365	+	2.30994i
$606$		0			0
$607$	16.7914	+	29.0836i	0.681544	+	1.18047i	0.974510	+	0.224345i	$0.0720244\pi$
$607$	16.7914	+	29.0836i	0.681544	+	1.18047i	−0.292966	+	0.956123i	$0.594642\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.03990	+	8.72936i	0.203892	+	0.353152i
$612$		0			0
$613$	8.18429	−	14.1756i	0.330561	−	0.572548i	−0.652061	−	0.758166i	$-0.726096\pi$
$613$	8.18429	−	14.1756i	0.330561	−	0.572548i	0.982622	+	0.185619i	$0.0594289\pi$
$614$		0			0
$615$	−34.8593			−1.40566
$616$		0			0
$617$	7.29657			0.293749			0.146874	−	0.989155i	$-0.453079\pi$
$617$	7.29657			0.293749			0.146874	+	0.989155i	$0.453079\pi$
$618$		0			0
$619$	19.4992	−	33.7736i	0.783740	−	1.35748i	−0.146009	−	0.989283i	$-0.546643\pi$
$619$	19.4992	−	33.7736i	0.783740	−	1.35748i	0.929749	−	0.368194i	$-0.120024\pi$
$620$		0			0
$621$	−13.5283	−	23.4317i	−0.542872	−	0.940282i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	13.8954	+	24.0676i	0.555818	+	0.962705i
$626$		0			0
$627$	−36.4659	+	63.1608i	−1.45631	+	2.52240i
$628$		0			0
$629$	−47.6096			−1.89832
$630$		0			0
$631$	−15.5523			−0.619127			−0.309563	−	0.950879i	$-0.600183\pi$
$631$	−15.5523			−0.619127			−0.309563	+	0.950879i	$0.600183\pi$
$632$		0			0
$633$	11.3466	−	19.6529i	0.450988	−	0.781135i
$634$		0			0
$635$	13.5571	+	23.4816i	0.537997	+	0.931837i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−15.9970	−	27.7077i	−0.632833	−	1.09610i
$640$		0			0
$641$	−15.3419	+	26.5729i	−0.605967	+	1.04957i	0.385930	+	0.922528i	$0.373881\pi$
$641$	−15.3419	+	26.5729i	−0.605967	+	1.04957i	−0.991898	+	0.127039i	$0.959453\pi$
$642$		0			0
$643$	16.3649			0.645369			0.322684	−	0.946507i	$-0.395415\pi$
$643$	16.3649			0.645369			0.322684	+	0.946507i	$0.395415\pi$
$644$		0			0
$645$	−90.3838			−3.55886
$646$		0			0
$647$	−12.1889	+	21.1119i	−0.479197	+	0.829993i	−0.999715	−	0.0238571i	$-0.992405\pi$
$647$	−12.1889	+	21.1119i	−0.479197	+	0.829993i	0.520519	+	0.853850i	$0.325739\pi$
$648$		0			0
$649$	−28.9866	−	50.2062i	−1.13782	−	1.97077i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.7341	+	23.7882i	0.537458	+	0.930905i	0.999040	+	0.0438072i	$0.0139487\pi$
$653$	13.7341	+	23.7882i	0.537458	+	0.930905i	−0.461582	+	0.887098i	$0.652718\pi$
$654$		0			0
$655$	−23.5765	+	40.8357i	−0.921210	+	1.59558i
$656$		0			0
$657$	−1.61837			−0.0631386
$658$		0			0
$659$	14.6757			0.571684			0.285842	−	0.958277i	$-0.407727\pi$
$659$	14.6757			0.571684			0.285842	+	0.958277i	$0.407727\pi$
$660$		0			0
$661$	15.8815	−	27.5075i	0.617717	−	1.06992i	−0.372184	−	0.928159i	$-0.621391\pi$
$661$	15.8815	−	27.5075i	0.617717	−	1.06992i	0.989901	−	0.141759i	$-0.0452757\pi$
$662$		0			0
$663$	−11.1386	−	19.2925i	−0.432585	−	0.749260i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.273118	+	0.473055i	0.0105752	+	0.0183168i
$668$		0			0
$669$	−9.64037	+	16.6976i	−0.372718	+	0.645567i
$670$		0			0
$671$	39.9681			1.54295
$672$		0			0
$673$	27.7181			1.06845			0.534226	−	0.845341i	$-0.320603\pi$
$673$	27.7181			1.06845			0.534226	+	0.845341i	$0.320603\pi$
$674$		0			0
$675$	31.3518	−	54.3029i	1.20673	−	2.09012i
$676$		0			0
$677$	8.31186	+	14.3966i	0.319451	+	0.553305i	0.980374	−	0.197149i	$-0.0631682\pi$
$677$	8.31186	+	14.3966i	0.319451	+	0.553305i	−0.660923	+	0.750454i	$0.729835\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.59336	−	4.49184i	−0.0993779	−	0.172128i
$682$		0			0
$683$	22.7423	−	39.3909i	0.870211	−	1.50725i	0.00843243	−	0.999964i	$-0.497316\pi$
$683$	22.7423	−	39.3909i	0.870211	−	1.50725i	0.861778	−	0.507285i	$-0.169351\pi$
$684$		0			0
$685$	−12.7633			−0.487661
$686$		0			0
$687$	32.6853			1.24702
$688$		0			0
$689$	−3.90233	+	6.75903i	−0.148667	+	0.257498i
$690$		0			0
$691$	−7.32451	−	12.6864i	−0.278638	−	0.482614i	0.692409	−	0.721505i	$-0.256549\pi$
$691$	−7.32451	−	12.6864i	−0.278638	−	0.482614i	−0.971046	+	0.238891i	$0.923216\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.87632	+	6.71398i	0.147037	+	0.254676i
$696$		0			0
$697$	−12.1459	+	21.0374i	−0.460060	+	0.796847i
$698$		0			0
$699$	12.1263			0.458658
$700$		0			0
$701$	20.9865			0.792649			0.396325	−	0.918110i	$-0.370286\pi$
$701$	20.9865			0.792649			0.396325	+	0.918110i	$0.370286\pi$
$702$		0			0
$703$	13.6821	−	23.6981i	0.516030	−	0.893791i
$704$		0			0
$705$	49.8422	+	86.3292i	1.87717	+	3.25135i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	21.0874	+	36.5245i	0.791955	+	1.37171i	0.924755	+	0.380563i	$0.124270\pi$
$709$	21.0874	+	36.5245i	0.791955	+	1.37171i	−0.132800	+	0.991143i	$0.542397\pi$
$710$		0			0
$711$	0.318027	−	0.550839i	0.0119269	−	0.0206581i
$712$		0			0
$713$	−3.48607			−0.130554
$714$		0			0
$715$	17.4263			0.651706
$716$		0			0
$717$	39.5068	−	68.4277i	1.47541	−	2.55548i
$718$		0			0
$719$	−1.43325	−	2.48246i	−0.0534512	−	0.0925802i	0.838062	−	0.545575i	$-0.183689\pi$
$719$	−1.43325	−	2.48246i	−0.0534512	−	0.0925802i	−0.891513	+	0.452995i	$0.850355\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.82178	+	4.88746i	0.104943	+	0.181767i
$724$		0			0
$725$	−0.632950	+	1.09630i	−0.0235072	+	0.0407156i
$726$		0			0
$727$	−3.92679			−0.145636			−0.0728182	−	0.997345i	$-0.523199\pi$
$727$	−3.92679			−0.145636			−0.0728182	+	0.997345i	$0.523199\pi$
$728$		0			0
$729$	40.3715			1.49524
$730$		0			0
$731$	−31.4922	+	54.5461i	−1.16478	+	2.01746i
$732$		0			0
$733$	−7.36097	−	12.7496i	−0.271884	−	0.470916i	0.697461	−	0.716623i	$-0.254313\pi$
$733$	−7.36097	−	12.7496i	−0.271884	−	0.470916i	−0.969344	+	0.245707i	$0.920980\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.86443	−	17.0857i	−0.363361	−	0.629360i
$738$		0			0
$739$	−19.0323	+	32.9649i	−0.700114	+	1.21263i	0.268312	+	0.963332i	$0.413534\pi$
$739$	−19.0323	+	32.9649i	−0.700114	+	1.21263i	−0.968426	+	0.249301i	$0.919799\pi$
$740$		0			0
$741$	12.8040			0.470369
$742$		0			0
$743$	45.4658			1.66798			0.833988	−	0.551782i	$-0.186052\pi$
$743$	45.4658			1.66798			0.833988	+	0.551782i	$0.186052\pi$
$744$		0			0
$745$	11.5951	−	20.0834i	0.424813	−	0.735798i
$746$		0			0
$747$	−23.9483	−	41.4797i	−0.876223	−	1.51766i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.20530	+	2.08763i	0.0439819	+	0.0761788i	0.887178	−	0.461427i	$-0.152662\pi$
$751$	1.20530	+	2.08763i	0.0439819	+	0.0761788i	−0.843196	+	0.537606i	$0.819329\pi$
$752$		0			0
$753$	−0.989856	+	1.71448i	−0.0360724	+	0.0624792i
$754$		0			0
$755$	49.7213			1.80954
$756$		0			0
$757$	−20.6065			−0.748955			−0.374477	−	0.927236i	$-0.622178\pi$
$757$	−20.6065			−0.748955			−0.374477	+	0.927236i	$0.622178\pi$
$758$		0			0
$759$	17.3195	−	29.9982i	0.628657	−	1.08887i
$760$		0			0
$761$	11.9677	+	20.7287i	0.433829	+	0.751414i	0.997199	−	0.0747905i	$-0.0238288\pi$
$761$	11.9677	+	20.7287i	0.433829	+	0.751414i	−0.563370	+	0.826205i	$0.690495\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−78.5290	−	136.016i	−2.83922	−	4.91768i
$766$		0			0
$767$	−5.08894	+	8.81431i	−0.183751	+	0.318266i
$768$		0			0
$769$	44.2135			1.59438			0.797189	−	0.603729i	$-0.206319\pi$
$769$	44.2135			1.59438			0.797189	+	0.603729i	$0.206319\pi$
$770$		0			0
$771$	−53.5417			−1.92826
$772$		0			0
$773$	−21.0458	+	36.4523i	−0.756964	+	1.31110i	0.187428	+	0.982278i	$0.439985\pi$
$773$	−21.0458	+	36.4523i	−0.756964	+	1.31110i	−0.944392	+	0.328821i	$0.893349\pi$
$774$		0			0
$775$	−4.03948	−	6.99658i	−0.145102	−	0.251325i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.98103	−	12.0915i	−0.250121	−	0.433223i
$780$		0			0
$781$	12.2321	−	21.1867i	0.437700	−	0.758118i
$782$		0			0
$783$	−4.17585			−0.149233
$784$		0			0
$785$	54.4875			1.94474
$786$		0			0
$787$	−7.54071	+	13.0609i	−0.268797	+	0.465570i	−0.968552	−	0.248813i	$-0.919959\pi$
$787$	−7.54071	+	13.0609i	−0.268797	+	0.465570i	0.699754	+	0.714384i	$0.253293\pi$
$788$		0			0
$789$	1.62954	+	2.82245i	0.0580133	+	0.100482i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.50844	−	6.07680i	−0.124588	−	0.215793i
$794$		0			0
$795$	−38.5922	+	66.8436i	−1.36872	+	2.37070i
$796$		0			0
$797$	50.5929			1.79209			0.896045	−	0.443962i	$-0.146428\pi$
$797$	50.5929			1.79209			0.896045	+	0.443962i	$0.146428\pi$
$798$		0			0
$799$	69.4656			2.45752
$800$		0			0
$801$	56.6607	−	98.1392i	2.00201	−	3.46758i
$802$		0			0
$803$	−0.618743	−	1.07169i	−0.0218350	−	0.0378193i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−42.7391	−	74.0263i	−1.50449	−	2.60585i
$808$		0			0
$809$	20.3447	−	35.2380i	0.715280	−	1.23890i	−0.247571	−	0.968870i	$-0.579632\pi$
$809$	20.3447	−	35.2380i	0.715280	−	1.23890i	0.962851	−	0.270032i	$-0.0870342\pi$
$810$		0			0
$811$	22.2066			0.779778			0.389889	−	0.920862i	$-0.372513\pi$
$811$	22.2066			0.779778			0.389889	+	0.920862i	$0.372513\pi$
$812$		0			0
$813$	−28.5717			−1.00205
$814$		0			0
$815$	−7.71033	+	13.3547i	−0.270081	+	0.467794i
$816$		0			0
$817$	−18.1005	−	31.3511i	−0.633258	−	1.09683i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.6815	+	27.1612i	0.547288	+	0.947931i	0.998459	+	0.0554934i	$0.0176732\pi$
$821$	15.6815	+	27.1612i	0.547288	+	0.947931i	−0.451171	+	0.892438i	$0.648993\pi$
$822$		0			0
$823$	7.17598	−	12.4292i	0.250139	−	0.433253i	−0.713425	−	0.700732i	$-0.752857\pi$
$823$	7.17598	−	12.4292i	0.250139	−	0.433253i	0.963564	+	0.267478i	$0.0861904\pi$
$824$		0			0
$825$	80.2756			2.79484
$826$		0			0
$827$	24.3504			0.846746			0.423373	−	0.905956i	$-0.360846\pi$
$827$	24.3504			0.846746			0.423373	+	0.905956i	$0.360846\pi$
$828$		0			0
$829$	15.8070	−	27.3786i	0.549001	−	0.950897i	−0.449343	−	0.893360i	$-0.648342\pi$
$829$	15.8070	−	27.3786i	0.549001	−	0.950897i	0.998343	−	0.0575378i	$-0.0183250\pi$
$830$		0			0
$831$	−2.44159	−	4.22896i	−0.0846978	−	0.146701i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−29.6357	−	51.3305i	−1.02558	−	1.77636i
$836$		0			0
$837$	13.3251	−	23.0798i	0.460583	−	0.797753i
$838$		0			0
$839$	41.4985			1.43269			0.716344	−	0.697747i	$-0.245814\pi$
$839$	41.4985			1.43269			0.716344	+	0.697747i	$0.245814\pi$
$840$		0			0
$841$	−28.9157			−0.997093
$842$		0			0
$843$	−20.9409	+	36.2707i	−0.721243	+	1.24923i
$844$		0			0
$845$	−1.52970	−	2.64951i	−0.0526231	−	0.0911459i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−10.6284	−	18.4089i	−0.364765	−	0.631792i
$850$		0			0
$851$	−6.49832	+	11.2554i	−0.222759	+	0.385831i
$852$		0			0
$853$	−48.1378			−1.64821			−0.824104	−	0.566439i	$-0.808321\pi$
$853$	−48.1378			−1.64821			−0.824104	+	0.566439i	$0.808321\pi$
$854$		0			0
$855$	90.2711			3.08721
$856$		0			0
$857$	−2.18112	+	3.77780i	−0.0745055	+	0.129047i	−0.900871	−	0.434087i	$-0.857071\pi$
$857$	−2.18112	+	3.77780i	−0.0745055	+	0.129047i	0.826366	+	0.563134i	$0.190404\pi$
$858$		0			0
$859$	17.6425	+	30.5577i	0.601954	+	1.04261i	0.992525	+	0.122042i	$0.0389442\pi$
$859$	17.6425	+	30.5577i	0.601954	+	1.04261i	−0.390571	+	0.920573i	$0.627722\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.6157	−	21.8510i	−0.429443	−	0.743816i	0.567381	−	0.823455i	$-0.307957\pi$
$863$	−12.6157	−	21.8510i	−0.429443	−	0.743816i	−0.996824	+	0.0796389i	$0.974623\pi$
$864$		0			0
$865$	−10.1328	+	17.5505i	−0.344525	+	0.596735i
$866$		0			0
$867$	−98.5714			−3.34766
$868$		0			0
$869$	0.486358			0.0164986
$870$		0			0
$871$	−1.73182	+	2.99960i	−0.0586804	+	0.101637i
$872$		0			0
$873$	16.6798	+	28.8902i	0.564525	+	0.977786i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.28331	−	10.8830i	−0.212172	−	0.367493i	0.740222	−	0.672363i	$-0.234720\pi$
$877$	−6.28331	−	10.8830i	−0.212172	−	0.367493i	−0.952394	+	0.304870i	$0.901387\pi$
$878$		0			0
$879$	14.4956	−	25.1071i	0.488924	−	0.846841i
$880$		0			0
$881$	−27.5910			−0.929564			−0.464782	−	0.885425i	$-0.653867\pi$
$881$	−27.5910			−0.929564			−0.464782	+	0.885425i	$0.653867\pi$
$882$		0			0
$883$	−24.9092			−0.838261			−0.419130	−	0.907926i	$-0.637665\pi$
$883$	−24.9092			−0.838261			−0.419130	+	0.907926i	$0.637665\pi$
$884$		0			0
$885$	−50.3272	+	87.1693i	−1.69173	+	2.93016i
$886$		0			0
$887$	7.41581	+	12.8446i	0.248999	+	0.431278i	0.963248	−	0.268613i	$-0.0865652\pi$
$887$	7.41581	+	12.8446i	0.248999	+	0.431278i	−0.714250	+	0.699891i	$0.753232\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	68.7578	+	119.092i	2.30347	+	3.98973i
$892$		0			0
$893$	−19.9631	+	34.5771i	−0.668040	+	1.15708i
$894$		0			0
$895$	7.79102			0.260425
$896$		0			0
$897$	−6.08128			−0.203048
$898$		0			0
$899$	−0.269016	+	0.465949i	−0.00897219	+	0.0155403i
$900$		0			0
$901$	26.8931	+	46.5803i	0.895940	+	1.55181i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.97148	−	13.8070i	−0.264981	−	0.458961i
$906$		0			0
$907$	24.3405	−	42.1589i	0.808212	−	1.39986i	−0.105889	−	0.994378i	$-0.533769\pi$
$907$	24.3405	−	42.1589i	0.808212	−	1.39986i	0.914101	−	0.405487i	$-0.132898\pi$
$908$		0			0
$909$	144.190			4.78249
$910$		0			0
$911$	−16.9244			−0.560730			−0.280365	−	0.959893i	$-0.590456\pi$
$911$	−16.9244			−0.560730			−0.280365	+	0.959893i	$0.590456\pi$
$912$		0			0
$913$	18.3121	−	31.7174i	0.606040	−	1.04969i
$914$		0			0
$915$	−34.6968	−	60.0966i	−1.14704	−	1.98673i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.6498	+	32.3024i	0.615201	+	1.06556i	0.990349	+	0.138594i	$0.0442584\pi$
$919$	18.6498	+	32.3024i	0.615201	+	1.06556i	−0.375148	+	0.926965i	$0.622408\pi$
$920$		0			0
$921$	11.5619	−	20.0257i	0.380976	−	0.659870i
$922$		0			0
$923$	−4.29499			−0.141371
$924$		0			0
$925$	−30.1196			−0.990327
$926$		0			0
$927$	−71.7616	+	124.295i	−2.35696	+	4.08237i
$928$		0			0
$929$	−11.9171	−	20.6410i	−0.390986	−	0.677208i	0.601594	−	0.798802i	$-0.294533\pi$
$929$	−11.9171	−	20.6410i	−0.390986	−	0.677208i	−0.992580	+	0.121594i	$0.961199\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−13.5410	−	23.4538i	−0.443314	−	0.767842i
$934$		0			0
$935$	60.0472	−	104.005i	1.96375	−	3.40132i
$936$		0			0
$937$	−45.3037			−1.48001			−0.740004	−	0.672602i	$-0.765177\pi$
$937$	−45.3037			−1.48001			−0.740004	+	0.672602i	$0.765177\pi$
$938$		0			0
$939$	−103.295			−3.37089
$940$		0			0
$941$	26.8932	−	46.5804i	0.876694	−	1.51848i	0.0217475	−	0.999763i	$-0.493077\pi$
$941$	26.8932	−	46.5804i	0.876694	−	1.51848i	0.854947	−	0.518716i	$-0.173590\pi$
$942$		0			0
$943$	3.31564	+	5.74286i	0.107972	+	0.187013i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.7547	+	22.0918i	0.414472	+	0.717886i	0.995373	−	0.0960879i	$-0.0306330\pi$
$947$	12.7547	+	22.0918i	0.414472	+	0.717886i	−0.580901	+	0.813974i	$0.697300\pi$
$948$		0			0
$949$	−0.108628	+	0.188149i	−0.00352620	+	0.00610756i
$950$		0			0
$951$	−61.2556			−1.98635
$952$		0			0
$953$	27.5063			0.891016			0.445508	−	0.895278i	$-0.353023\pi$
$953$	27.5063			0.891016			0.445508	+	0.895278i	$0.353023\pi$
$954$		0			0
$955$	19.1133	−	33.1051i	0.618491	−	1.07126i
$956$		0			0
$957$	−2.67305	−	4.62985i	−0.0864074	−	0.149662i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.7831	+	23.8731i	0.444618	+	0.770100i
$962$		0			0
$963$	−69.5670	+	120.494i	−2.24176	+	3.88285i
$964$		0			0
$965$	50.8335			1.63639
$966$		0			0
$967$	−16.0644			−0.516596			−0.258298	−	0.966065i	$-0.583162\pi$
$967$	−16.0644			−0.516596			−0.258298	+	0.966065i	$0.583162\pi$
$968$		0			0
$969$	44.1200	−	76.4181i	1.41734	−	2.45490i
$970$		0			0
$971$	21.8129	+	37.7811i	0.700011	+	1.21245i	0.968462	+	0.249161i	$0.0801549\pi$
$971$	21.8129	+	37.7811i	0.700011	+	1.21245i	−0.268451	+	0.963293i	$0.586512\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.04667	−	12.2052i	−0.225674	−	0.390879i
$976$		0			0
$977$	−15.2636	+	26.4373i	−0.488325	+	0.845804i	−0.999910	−	0.0134288i	$-0.995725\pi$
$977$	−15.2636	+	26.4373i	−0.488325	+	0.845804i	0.511585	+	0.859233i	$0.329059\pi$
$978$		0			0
$979$	86.6511			2.76938
$980$		0			0
$981$	14.4396			0.461019
$982$		0			0
$983$	13.5965	−	23.5498i	0.433660	−	0.751121i	−0.563525	−	0.826099i	$-0.690555\pi$
$983$	13.5965	−	23.5498i	0.433660	−	0.751121i	0.997185	+	0.0749777i	$0.0238885\pi$
$984$		0			0
$985$	−27.3186	−	47.3171i	−0.870442	−	1.50765i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.59686	+	14.8902i	0.273364	+	0.473481i
$990$		0			0
$991$	−0.0450891	+	0.0780966i	−0.00143230	+	0.00248082i	−0.866741	−	0.498759i	$-0.833789\pi$
$991$	−0.0450891	+	0.0780966i	−0.00143230	+	0.00248082i	0.865308	+	0.501240i	$0.167123\pi$
$992$		0			0
$993$	11.8420			0.375796
$994$		0			0
$995$	39.9137			1.26535
$996$		0			0
$997$	−26.8383	+	46.4854i	−0.849979	+	1.47221i	0.0312474	+	0.999512i	$0.490052\pi$
$997$	−26.8383	+	46.4854i	−0.849979	+	1.47221i	−0.881226	+	0.472695i	$0.843281\pi$
$998$		0			0
$999$	−49.6781	−	86.0450i	−1.57175	−	2.72234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.j.r.1145.6		12
7.2	even	3	inner	2548.2.j.r.1353.6		12
7.3	odd	6		2548.2.a.r.1.6	✓	6
7.4	even	3		2548.2.a.s.1.1	yes	6
7.5	odd	6		2548.2.j.s.1353.1		12
7.6	odd	2		2548.2.j.s.1145.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.a.r.1.6	✓	6	7.3	odd	6
2548.2.a.s.1.1	yes	6	7.4	even	3
2548.2.j.r.1145.6		12	1.1	even	1	trivial
2548.2.j.r.1353.6		12	7.2	even	3	inner
2548.2.j.s.1145.1		12	7.6	odd	2
2548.2.j.s.1353.1		12	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61626 - 2.79944i) q^{3} +(-1.52970 - 2.64951i) q^{5} +(-3.72458 - 6.45116i) q^{9} +(2.84800 - 4.93288i) q^{11} -1.00000 q^{13} -9.88953 q^{15} +(-3.44578 + 5.96827i) q^{17} +(-1.98051 - 3.43034i) q^{19} +(0.940643 + 1.62924i) q^{23} +(-2.17993 + 3.77576i) q^{25} -14.3820 q^{27} +0.290353 q^{29} +(-0.926514 + 1.60477i) q^{31} +(-9.20620 - 15.9456i) q^{33} +(3.45419 + 5.98283i) q^{37} +(-1.61626 + 2.79944i) q^{39} +3.52487 q^{41} +9.13934 q^{43} +(-11.3949 + 19.7366i) q^{45} +(-5.03990 - 8.72936i) q^{47} +(11.1386 + 19.2925i) q^{51} +(3.90233 - 6.75903i) q^{53} -17.4263 q^{55} -12.8040 q^{57} +(5.08894 - 8.81431i) q^{59} +(3.50844 + 6.07680i) q^{61} +(1.52970 + 2.64951i) q^{65} +(1.73182 - 2.99960i) q^{67} +6.08128 q^{69} +4.29499 q^{71} +(0.108628 - 0.188149i) q^{73} +(7.04667 + 12.2052i) q^{75} +(0.0426930 + 0.0739465i) q^{79} +(-12.0713 + 20.9080i) q^{81} +6.42980 q^{83} +21.0840 q^{85} +(0.469285 - 0.812826i) q^{87} +(7.60632 + 13.1745i) q^{89} +(2.99497 + 5.18744i) q^{93} +(-6.05915 + 10.4948i) q^{95} -4.47830 q^{97} -42.4304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{5} - 6 q^{9} + 4 q^{11} - 12 q^{13} + 8 q^{15} - 16 q^{17} - 10 q^{19} + 2 q^{23} - 12 q^{25} - 24 q^{27} + 4 q^{29} - 6 q^{31} - 28 q^{33} - 16 q^{37} + 16 q^{41} + 12 q^{43} - 34 q^{45} - 30 q^{47}+ \cdots - 104 q^{99}+O(q^{100}) \) 12 * q - 10 * q^5 - 6 * q^9 + 4 * q^11 - 12 * q^13 + 8 * q^15 - 16 * q^17 - 10 * q^19 + 2 * q^23 - 12 * q^25 - 24 * q^27 + 4 * q^29 - 6 * q^31 - 28 * q^33 - 16 * q^37 + 16 * q^41 + 12 * q^43 - 34 * q^45 - 30 * q^47 + 12 * q^51 + 6 * q^53 - 32 * q^55 - 24 * q^57 - 8 * q^59 - 16 * q^61 + 10 * q^65 + 8 * q^69 - 14 * q^73 - 28 * q^75 - 14 * q^79 - 14 * q^81 - 28 * q^83 + 48 * q^85 - 24 * q^87 - 30 * q^89 + 16 * q^93 + 10 * q^95 + 44 * q^97 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more